An antisymmetric tensor is defined as a Tensor for which

(1) 
Any Tensor can be written as a sum of Symmetric and antisymmetric parts as

(2) 
The antisymmetric part is sometimes denoted using the special notation

(3) 
For a general Tensor,

(4) 
where
is the LeviCivita Symbol, a.k.a. the Permutation Symbol.
See also Symmetric Tensor
© 19969 Eric W. Weisstein
19990525